Biology / An elementary 5-dimensional model applied in different sciences
The Cell

1. Some general aspects:

1. A cell is a complex center, a "0-pole" in relation to its environment. At the same time it is a whole in itself, as dimension degree (d-degree) 5, ~ 0/00 in the background model applied here - including all the geometrical polarities of the dimension chain.
   Chemical substances could be regarded as both building workers and building blocks that substantiate and illustrate an underlying drawing.
   The enormous complexity in a cell seems only possible to understand if we regard it as results of internal polarizations within some already enclosed unit with a substantiated anticenter, an original structure of type 0/00, center/anticenter (c/ac); the complexity a result of opposite, internal forces.
   (Which kind of center, which kind of anticenter when first cell appeared?)

2. Why a relation between DNA or RNA and proteins as a genetic code?

It's one main question. Here the c - ac relation between C-atoms in tetrahedrons of amino acids (ams) versus rings of the codon bases are stressed.
   It is suggested that the relation can be illustrated with the hexagonal pattern below. Imagine a layer of graphite, or - with virtual free valences upwards next layer - a crashed diamond. (All substituents to C-atoms dismissed.)
   Carbon rings, sharing edges, and centers with 3 radii (+ the virtual 4th) become two aspects on the same whole pattern. Two ways of reading.
   (Other main classes of substances sketched as well.)

Fig C-1-7-Hex

One center with 3 radii is defined by 3 rings - as amino acids by codons.
   The horizontal peptide in the figure above can illustrate how side chains of amino acids must point in opposite directions for each amino acid to get a separate triplet of bases. Codons too get opposite directions:


Fig C-8-Hex
(Eventual implication for interpretation of proteins?)

Fig C-9-Hex

Amino acids (3 of them) give main contributions in synthesis of the bases. The simplest amino acid Gly makes up the very center at synthesis of the purine bases A and G. Asp makes up about half the pyrimidine bases. (Moreover, an amino acid as Ile is used in synthesis of fatty acids.)

One 6-ring in the bases gives theoretically, 2 x N-C-C, the bound backbone chain in an amino acid. (See further The protein synthesis.)
   Mean mass value of a codon base (RNA) is 126 +1, 6 x 21 +1. Mean value of a side chain of amino acid is approximately half this number, 63, 3 x 21. (About "A-Z"-numbers here.).
   3 units with a central C-atom and 3 radii shape a 6-ring. Cf. about mass number transformations in the genetic code where 8 bases give the backbone chains or side chains of 24 amino acids, a relation 1/3.   

RNA-chains have been found to possess a certain catalytic capacity, which may be easier to understand with the hexagonal illustration.
   In our cells it's the halving of 6C carbohydrates (however transformed to 5C rings + 1C, fructose) that through glycolysis and citrate cycle leads to synthesis of fatty acids and amino acids respectively.
About fatty acids, the illustration can be compared with the fact that the double layer of lipids in cell membranes at a certain temperature (~ 37°) get hexagonal structures, an unstable state of phase transitions (Zf).

The figure doesn't include pentagon rings, the extra 3 edges in purine bases, not differences in angles of valences, nor any substituents. With the figure above it's not the intention to assert that this was 'the way it happened'. Yet, it may illustrate the close relations between substances and the underlying two aspects on the whole structure: a pattern of rings or a pattern of centers with 3 radii.

The idea of a crashed diamond leads to the thought of different substances created from the different ways and diffraction of light in a crystal.

A speculation about phase waves - a very abstract thought:
From a hypothetical reasoning in a file on physics it could perhaps be possible to apprehend proteins (and other classes of substances) as a kind of "phase waves" on a superposed, substantiated level: expressions for relations between other substances as "waves" . Or DNA (RNA) as materialized phase waves between protein chains? (Cf. about the Balmer series for spectral lines of hydrogen, fig 1-1.) It contradicts of course scientists' opinion that such waves don't contain any information.
   (If the mass numbers of codon bases could be associated with d-degrees or steps between d-degrees in different ways, see the Genetic code, and these steps also include angle changes, then the relation between the nucleotides as "rotating vectors" could give birth to phase waves? Such waves - or complex relations between them, could be imagined to decide the row of amino acids in a protein - or follow from them?)

3. The protein synthesis:

Compared with the view in the hexagonal pattern above and the very close c/ac-relation amino acids/bases, the synthesis of proteins in a developed cell appears as a much more complicated process "the other way around":

 Fig C-10

Illustrated according to the loop version of the model - or as in a circle:

Fig C-12


One theory among scientists about origin of the genetic code assumes a preceding stage of close connection between codons and amino acids before the transcription system developed. In secondary forms a close relation appears in DNA rolled up on histones, in ribosomes and in tRNAs, binding individual amino acids etc. Could perhaps the existence of the special membrane-enclosed nucleol within the very nucleus of the cell, at a certain chromosome, containing material for the ribosomes (rRNA), reveal something about such an underlying origin of closer dependence?

Why this complicated, circumventing process to produce proteins? While amino acids directly engage in constructing bases, contributing most of them, the way from bases (ac-pole ~ 00) to amino acids (c-pole ~ 0) becomes very different, a "code", as a reference over the distances created by the separation.
   One aspect with reference to the dimension model could be that outward direction from a 0-pole (c →>ac) implies radial structure in d-degree 3, while inward direction from a 00-pole appears as 'circular'. These complementary geometric forms could have decided the geometry of the very processes (?).

4. A cell as inversion of an atom:

The cell as the "elementary particle" of biology can be interpreted as an inversion of an atom. Its outer cell membrane may be seen as a potential barrier, an inversion of the nuclear, strong force (FST).
- The lipid bilayer membranes keep together solely by hydrophobic bonds, an H+-aggregating, gluey force, while proteins, DNA and other inner structures are built by the covalent force between atoms with unsaturated electron (e-) shells. (About views on chemical forces here.)
   H+ and e- become elementary "carriers of forces" on the chemical level.

- Charges are reversed, with relative negative charge on inside, positive on outside.
(Positive (+)-charge seen as originating from inward direction, negative (-)-charge from outward direction.)

A cell membrane as a surface is "semipermeable". It's characterized by changing phases or degrees of permeability. Permeability as a physical quantity is inversely proportional to charge squared. CF. d-degree 2 as surfaces and charge in this model assumed as a 2-dimensional physical quantity.

- A cell in its main structure shows also a reversed relation mass - space in the relative sense of phases: membranes as anticenter of the cell around inner space. In atoms the protons (H+) represent most of the mass, while outer electron shells make up most of the atomic space.

About other suggested inversions, see file 1/7, and mass number 544 in the genetic code as from the inverted p/e quotient.

(All physical forces, which in these files are interpreted as developed out of one another, must reasonably be expected to appear in the cell in their chemical versions. And naturally, a cell can be described in all physical quantities interpreted as steps in a dimension chain. (Density introduced as a first such quantity defined by the polarization center - anticenter, in later step expressed as mass per volume, in step 1→>0/00 as distance per time and frequencies.

Fig 13-145-1 )

5. Proteins - Lipids, the macro-level structure:

In the cell, on its macro-level, the proteins come to form the main radial structure, the cytoskeleton, while the fatty acids as lipids make up the roughly circular structures, the primary cell membrane ( in eukaryotic cells the nuclear membrane, the endoplasmic reticulum (ER), Golgi apparatus etc.)
   It's the two main structure-building parts of the cell and the geometrical polarity radial - circular as poles out of d-degree 3 in the dimension chain.
   (It's not the whole truth, since protein threads are also found as "horizontal" layers inside lipid membranes an as nets outside these on some kind of cells. Yet a main polarity.)

   Fig 14-143-1

Protein threads as F-actin and microtubuli stretches radially outwards through cytoplasm and likewise in cilia and microvilli. Other proteins form the radial canals in lipid membranes. They function as infrastructure and transport tracks, as for instance spindles at cell division obviously also as vectors.
   At protein synthesis the peptide chains grow 'straight through the walls' of lipid membrane
in the endoplasmic reticulum in a way that feels curious, if not founded in a basic geometry.

Radial structures are principally unlimited outwards, circular structures closed. It's the same polarity as between electric and magnetic field lines E and M. Cf. in file about forces relations to protons (p) and electrons (e) within plasma physics:
   p ~ M2
   e ~ E2
Hence,we find a connection between magnetic fields squared, protons (H+) and the closed H-bonded lipid membranes of a cell, as between electric fields squared, electrons (e-)and covalent bonds of proteins.
   The fact that the cell membrane in itself is a structure of both kinds, containing about 50 % proteins, 50 % lipids, could remind of light beams with their regular phase displaced changes between E- and M-factors. Compare again possible readings in figure 1 above.

In the dimension model the radial and circular poles of d-degree 3 may be seen as derived from 0- and 00-poles respectively in a haploid chain, illustrate in the figure below, however somewhat misleading: the steps for lipids sooner should be angled more perpendicular to the steps for proteins.
   Amino acids in protein derive from molecules of 5 - 4 - 3 C (carbon), while the synthesis of fatty acids is a repetitive process in step 3 - 2: (3 C -1 C→> 2 C) to n x 2 C. (Cf. 2 as d-degree of a border, a surface.) It's a synthesis on a multienzyme complex with amino proteins involved and amino acid Cys providing the HS-sites for attachment during the process..(Cf. Cys, mass of side chain 47 A, total mass of side chains of amino acids from 24 differentiating codons = 32 x 47.)

      Fig C-15

In geometrical macro-structure the lipids develop in steps 1 - 2 - (3): from linear fatty acids, d-degree 1, to 2-dimensional when with backbone chain of glycerol (3 C) to the spherical membrane enclosing 3-dimensional volumes, demarcating different phases and rooms.
   About glycerol and polarization of carbohydrates, 6 C, into 2 x 3 C, see below.

An essential process as from middle step 3 - 2 is the Pentose-phosphate cycle, that implies transformation of 5 x 3C into 3 x 5 C (note number 15, sum of d-degrees in the dimension chain), where one way is 6C - 2C to 4C, + 3C to 7C, - 2C. (7 = sum of poles in d-degrees 3 an 2.)
   It can be added that when plants build in 1C from the air in a 5 C carbohydrate to 6C, it is in the middle between 3rd and 2nd C-atom.

[About classes of substances on the molecular level here.]

6. L-waves, T-waves and subunits:

Fatty acids as subunits of lipids have a similarity with longitudinal L-waves, although in a zigzag shape. (Cf. perhaps the movements of single P-lipids along the membrane during its fluid phase.) Protein chains, unfolded, with their side chains of amino acids, correspond in a similar way to transversal T-waves.
   It's presumed in the model that L-waves as linear, 1-dimensional, [→ ← → ← → ← ...] are connected with forces FG and FA, gravitation and the complementary outward acceleration force. These represent d-degree 4 in a dimension chain of forces and are interpreted as polarized into positive and negative (rather antipositive) curvature in step 4 →> 3 in the model here and appear in the polarity Mass and Space in terms of physical properties.
   Membranes are connected with the polarity Mass - Space in the secondary sense of differentiating phases. Their H+-bonds (methyl bonds), connected with mass, are identified as pole 4a among chemical forces, i.e. inward direction. The bilayers, however, of fatty acids in membranes can in fact be seen as illustrating both the inward and outward directions of d-degree 4.
   (Cf. about linear waves as motions in section 8 below.).)

T-waves are exemplified by the more well-known electromagnetic waves and the force FEM,
[↓ → ↑ ← ↓ → ↑ ← ↓ →↑...] with the complementary electric and magnetic factors FE and FM. It's presumed as a force developed in following step 3 - 2 in the model.
   The covalent bonds in proteins are identified as pole 4b in the dimension chain of chemical forces, implying outward direction. Peptide bonds include polarity of charge (NH3+ ↔ COO-) and represent the L-factor in proteins as T-waves.

With these identifications the lipids come to represent a deeper, underlying level in relation to the proteins, where we for instance also have an angle step in the phase displacement between field components from 180° to 90°.
   How to regard this contradiction? The only way (?) seems to be to regard debranched degrees from higher steps meeting "the other way around" in accordance with the loop model .


Fig C-16

As waves proteins and lipids should correspond to a substantiation of the dimension chain of motions:
- Step 5 → 4, physical quantity Density proposed, 1 degree debranched, linear waves as polarizations of density. (Bilayer of P-lipids as micells appear at higher density.)
- Step 4 → 3, Direction, d-degree 4, polarized to a perpendicular angle , 90°: T-waves, 2-3-dimensional depending on aspect.

Both wave types contain the features of both poles of the higher d-degrees→ 4 → 3. Backbone chains of the proteins (typo L-waves but expressed in quantity charge, d-degree 2) become expression for divergent inner space (pole 4b), sustaining it as radial cytoskeleton.

Fig C-17

Waves as such could probably be best understood as the sewing together of the two complementary fields in each d-degree.

If the aspects above on lipids and proteins as corresponding to the polarity between L- and T-waves, it leads naturally to other speculations. See section 8 below..

(It has to be added here that Archae bacteria, assumed as the oldest unicellular phyla, uses isoprenes, molecules of 5C, instead of fatty acids of n x 2C in their membranes. It implies carbon groups as a kind of transversal factors in their lipids too.)

7. Polarizations into complementary "poles"?

According to the dimension model a developed cell should be possible to interpret as the result of polarizations into complementary "poles" as partial structures in different -degrees and on a lot of levels. When it concerns the elementary definitions: opposite vector directions, mass - space, charges +/-, outside - inside, divergent - convergent motions etceteras, all kinds of complementary polarities can too easily be found in a cell - but how about classes of substances on a more concrete level?

Carbohydrate - fructose:
The most obvious example is the division of carbohydrates: the halving of an hexose (fructose), leading to lipids and amino acids of proteins, i.e., the main circular versus radial structures of the cell.
   Two 3C pyruvate +/-1 C gives
C4 (note sign +, inwards) to mitochondria to oxaloacetate in citrate cycle (note a cycle), and
b) outwards (sign -) C2, Acetyl(~Coa,) leading to to fatty acids and isoprenes.

      Fig C-18

In this process the glycolysis also gives the polarity between perpendicular parts of triglycerides (glycerol versus fatty acids).


Fig C-19-147-1

In a secondary or synthesizing way we find the branching from Acetyl(~CoA) to elements in the two classes fatty acids, (the repeated process C3 - C1 to n x C2), and isoprenes/steroids (3 x C2 - C1 to n x C5). The amino acids Ileu and Leu that only differ stereometrically, contribute to fatty acids and steroids respectively.
   (The ways for Acetyl(~CoA) has also a preceding ramification, where one joins the citrate circle, the "protein way", leading back to 6C - 5C molecules, here as keto acids.)

The division of a carbohydrate as fructose leads to different classes of substances. When it concerns internal polarizations within the classes, DNA seems to be the only (?) or most obvious structure that corresponds to an unpolarized "d-degree".
   It's opposite strands represent codons of mRNA and tRNA gets polarized into complementary units or "poles"; meeting "the other way around" on ribosomes as mRNA →> ← tRNAs at the protein synthesis.
   The opposite directions of strands lengthwise and the complementary forms of the bases underline the polarities as does the complementary syntheses of the bases.

Complementary directions in structures:

Within classes the most obvious examples of opposite directions in structures are DNA strands and bilayer of lipid membranes between inner and outer rows of P-lipids.
   There are striking similarities between these two molecular compounds with very different functions. Both consist of a) P-group, b) a carbohydrate element, c) then the specialized molecular objects: codon bases and fatty acids respectively:

P-group → deoxiribose → base —> H-bridge <— base ← deoxiribose ← P-group
P-group → glycerol → fatty acids —> H-bonds <— fatty acids ← glycerol ← P-group

The POxHx-groups surround both structures as "first and last" elements - as do the poles 0 and 00 out of d-degree 5 in the dimension model.
   Notice P-atom, valence 5. and d-degree 5, polarized 0 - 00, origins for primary binding and polarizing forces in the model. (Cf. too fructose-6-phosphate that first when enclosed between two P-groups in fructose 1,6-bisphosphate can be halved by an enzyme.)
   Another similarity may be seen in the perpendicular, vertical - horizontal bonds between P-groups and the carbohydrate part.
   Simultaneously there is the principal difference between "linear" structure of glycerol and fatty acids in lipids and the ring closed corresponding parts in DNA, like a step from d-degree 1 to 2. And ribose in DNA, 5C, presupposes the pentose-phosphate cycle 5 C3 →> 3 C5.

About the different parts, it seems that the complementary relation between inner bases of the DNA-structure above could have correspondences in the outer, different kinds of attached molecules to "heads" of P-lipids on inner and outer layers respectively of membranes (Wikipedia, Lipid_bilayer).

We can also remember how the chains of fatty acids of lipids arrange in hexagonal patterns - like the one in codon bases - during certain phases. Geometrically it appears as a d-degree step 1 to 2.

The correspondence between these central versus anticentral constructions needs certainly a better interpretation.
   One view in terms of valences, to compare with the figure above on lipids and proteins as L- and T-waves. C - H valences 4 --- 1, N - O valences 3 - 2:

      Fig C-20

Polarities within lipids and proteins:
Compared with DNA a similar structural division of lipid membranes seems not to exist (?). If there is any complementary features between P-lipids of inner versus outer layer, in origin or construction, it doesn't seem recognized yet. There is however other kinds of internal polarities:
   One is the transition between phases, which both can exist simultaneously on different parts of the membrane: the solid gel phase and the fluid one - as if area of the membrane had inherent subdivisions (?).
  Another opposition is the just mentioned changes between ordinary and hexagonal structures (Zf p. 181).

A third feature, more adequately identified as a polarity, is the ability of lipid layers to form "plain and purl" structures, heads outwards or inwards: the polarity of directions out of d-degree 4. It's also a polarity of charge out of d-degree 2 in the model. The geometrical polarity of d-degree 2 has been defined elementary as outside/inside. On a macro-scale the bilayer membrane illustrates it. The sense or function, if any, of such inversions seems not clear.
   One older observation was that fragmented membranes of mitochondria appeared some with "knobs" on the outside, some with these knobs on the inside, thus examples of such polarities and inversions.

Evaginating/invaginating parts of the membrane forming vesicles illustrate one kind of 3-dimensional motion, assumed in structures of d-degree 2 and at the same time the polarization of directions of d-degree 4. Cf. meteorology: high and low pressure cells debranched from Rossby waves around the North Pole.

Among proteins, there are one main polarity between synthesizing and breaking enzymes.
   Another fundamental one seems to be the one between proteins as transporting vehicles, some transporting molecules outwards, some inwards - as kinesin and dynein in cilia tubuli. They illustrate the opposite vectors of d-degree 4. (It would be very interesting to know which factors, amino acids or codons or other factors in such specialized proteins that are decisive for their complementarity.)
   Certainly many other such examples of complementary proteins exist, also acting on long distances from one another. Are such complementary pairs of proteins eventually a fundamental principle rooted in the genes?
   Human genome includes more than 100,000 proteins, while number of genes is only about 28,000 according to some data. It means that one gene on average should code for about 4 proteins. Through different frames at transcription or different cuttings of mRNA before? Do proteins from the same gene eventually show on polar relations in their functions?
   It's hard to imagine any common x-dimensional unity as origin for complementary proteins, if not in opposite pieces of DNA-strands or perhaps in complementary folding?

(About classes of substances in cells, see further Biochemistry.).

8. Speculations:

About L- and T-waves:
If we accept the hypothetical view in No. 6 above on fatty acids and proteins as substantiated L- and T-waves, and these are taken as connected with the pairs of forces FG - FA and FE - FM respectively, it awakes two kind of questions.

    Fig C-21
   Fig C-22

A first question is if proteins in any way or sense could be seen as derived from or later than lipids (!) as lower d-degrees from higher ones? Nothing in actual, internal biochemistry of a cell supports such a view. As atoms N and O derive from C in the carbon-nitrogen cycle of fusion in the sun but that's another history. Could some first amino acids have been constructed on, in or between bilayers of P-lipids? We can only point to some close relations: the attachment of ribosomes to membranes when protein synthesis occurs, the protein chains growing straight in through the membranes of the endoplasmic reticulum, processed further within the membrane enclosed rooms, as in the Golgi apparatus - and the ~50 % proteins curiously 'interrupting' the outer cell membrane itself.

The second question is if expressions for the pairs of connected forces in some way can be identified in the lipids and proteins.
   About lipids, we could ask if the inner layer of a bilayer membrane differs in some essential but hidden way from the outer layer, in kinds of fatty acids or something else, mirroring the opposition between space and mass, between forces FA and FG? There is the above mentioned inversions in directions that nets of P-lipids can undergo with P-groups inward or outwards. (When? Under which conditions? If it is or gets explained, what could it eventually tell us about this relation FA - FG in macrocosm?

Perpendicular to direction of a lipid, along the membrane,,,, L-waves seems expressed in motions: There is the curious fact that in the fluid phase "a given lipid will exchange locations with its neighbor millions of times a second" and thus can wander along the membrane (Wikipedia: Lipid_bilayer). Is this behavior really necessary! Biochemically? It sooner seems as just an illustration of an L-wave → ← → ← → ← and the pole exchanges in d-degree 0/00 of Motions in the dimension model.
   In the model we have structure of a certain d-degree plus debranched d-degree as external motion. Regarding the fatty acids as substantiated structures of L-waves, the debranched d-degree - in a step from higher Density ( 5 →> 4) to lower - could get this expression?

About proteins, they should illustrate the relation between FE and FM, the electric and magnetic forces or factors of FEM. Besides their role as cytoskeleton, like a static EM-field, they may be said to represent a communication system, distributed long ways as are EM-waves.
   We could ask if any of the many polarities between amino acids or their codons in some way represents the opposition M-fields versus E-fields with some functions related to circular versus radial geometries? Surely an odd and here unanswered question. It's easier to imagine the relation between purine and pyrimidine bases of codons in terms of E- versus M-components (G,A versus U, C or ?).

About amplitude versus frequency modulations:

Isolating the features of inward - outward directions in membranes versus proteins, it may be asked if the polarity between amplitude and frequency modulation in some way could be applied on these substances. In atoms the absorbed incoming energy of photons get translated to higher, "circular" amplitude of electron orbitals, while frequency of emitted energy are decided by radial electron jumps between orbitals. In nervous signals we have the similar polarity: amplitude modulation of incoming signals through dendrites of the nerve cell, note spread in its membrane, and frequency modulation in outgoing responses through its axons towards other cells.
   The genetic code is a "language" and the 20 classical amino acids correspond in number roughly with number of phonemes in different languages, phonemes which are different combinations of frequencies.
   Lipid membranes are difficult to study and hitherto they don't seem to be attributed much of individualized properties by scientists. However, the different membranes of nucleolus, the nucleus, the endoplasmic reticulum, the Golgi apparatus and cell membrane represent roughly different amplitudes. Could their positions eventually give them some hidden but essential differences that decide their roles for different processes and metabolism? One example is perhaps that certain parts of ER attract ribosomes. A more obvious one is the Golgi apparatus, where protein chains are undergoing different modifications within the different apartments outwards: why these steps in the modifications?

   Elementary sketch of membrane amplitudes. Fig 23-147-2


9. A cell as substantiation of motions:

In a dimension chain of structures outwards, the debranched degrees transformed to external motions come to form a dimension chain in opposite direction inwards. This according to the elementary postulates in the dimension model.
   It awakes the thought that a cell would be best understood as a substantiation of this inward directed chain of motions, in this sense also an "inversion" of the atom (cf. No. 4).   

   Fig C-24

Related is the fact that most structure-building in the cell occurs as steps inwards, from single units to linear additions to 2-3-dimensional structures of the type 3← 2←1← 0.
   Among the multitude of motions there are the high mobility of cell membranes, invaginations and evaginations as 3-dimensional motions (~ convex/concave as one polarity of d-degree 2) and contractions/relaxations of protein threads as a kind of 1-dimensional vibration.
   Nucleus and other organelles of a cell can also move around in the cell (cf. "translational motion in 3 directions?) and even rotate. The cytoplasm itself is continuously streaming in different directions (Fb p. 10).
   The whole cell as a prison for trapped motions?

The metabolism of cells with nourishment from its environment corresponds to the presumed "breathing" of atoms, i.e. how atoms uphold their existence and structure through "breathing" of what is antimatter on their level - the surrounding "empty" space. Structure of matter breaks down when gravitation of Mass chokes the access to Space. Cf. the interpretation of light waves too.

10. About number 5 - as dimensions in the model:

- One, most elementary example is valence 5 of the P-atom: the HxPOx-groups having organizing and energy-storing functions in the cell.
   (Could inorganic phosphorus eventually have served like a grain for growth of snow crystals, when a cell appeared?)

- A second example is ribose, the 5C-molecule of carbohydrate, essential in .nucleotides. As mentioned above the Pentose-phosphate cycle transforms 3 ribose C5 to 5 C3-molecules. There we have the number 15, sum of the d-degrees in the dimension model Cf. HCOH = 30 A, sum of poles in the model.

- Another 5C-molecule is isoprene, three of which join to one C15 and these may join head to head, i.e. in opposite directions to form squalene of C30 on the way to steroids; 30 the sum of outer complementary a- and b-poles in our model.
   Mentioned above too is the old, single-cell Archae bacteria, which uses isoprenes to create fatty acids (Wikipedia). As two C15 molecules can meet head to head, so can these isoprenes of Archae join their tails in a similar way.

- On the level of organelles it has been found that ribosomes, where protein synthesis occur,
appear usually in groups of about 5 in bacteria (Bc p. 79). Ribosomes are also very old organelles, compounds of RNA and proteins (cf. figure 1!).

- The Golgi apparatus in eukaryotic cells is described as most often consisting of 5 - 6 christae (Aph), membrane enclosed apartments or factory sections.

- Another kind of example could be the number of enzymes, 5, involved at copying of DNA to mRNA, a process demonstrated by Roger Kornberg and his team at Stanford about 2007.

- Finally we could remind of the 4 - 5 cyclic processes that scientists (e.g. Marquand) have considered as necessary conditions for life.

About cancer
, some very abstract thoughts.
Development of cancer has been said to occur in 4-5 steps.

      Fig C-25-154-1

0-pole is defined as primary, integrating binding force in the dimension model, 00-pole primary polarizing force. The 0-pole is also the one of unity, the 00-pole the one of multiples.

Experiments with "exogastrulation" in development of embryos showed that the cells of the animal pole (~ 00-pole) when tied off from the vegetative pole only developed to an amorphous, hollow mass, while the cells from the vegetative pole (~ 0-pole) differentiated towards different organs, although not complete.
   Cancer as amorphous, undifferentiated cell divisions could thus correspond to the result of an isolated 00-pole, its uninhibited, unregulated divisions when the 0-pole as integrating binding force has been weakened.
   The observation that cancer cells often first appear in rings (Aage Möller 1974, lecture) seems to support the analogy with exogastrulation. It's also said that pregnancy can have a suppressing effect on cancer - perhaps because an embryo represent a vigorous center.

A 0-pole, a center, gives outward direction as integrating force, which could correspond to field lines from a cell outwards towards other cells. A 00-pole, an anticenter, gives inward direction as a polarizing and isolating force.
   Mutagen, carcinogenic chemical substances contain for instance often CHx-groups which give inward direction (aromatic, ring-shaped carbohydrates too, in molecular structure inward directed). Cf. for instance the T-base = U-base plus a CH2-group that turns a strand of nucleotides inwards to DNA. Characteristic for cell division in opposition to interphase is duplication of DNA with T-base instead of U as in mRNA.
   A cancer cell leaves the tissue level of organization and 'casting', the distribution of roles, and returns to the cell level. In the big chain of levels this is also a direction inwards, towards underlying level compared with the cell as part in a bigger whole.
   In this respect cancer would be about the same as the relation between unicellular and multicellular organisms. (Which proteins or genes separate these classes?) Cancer can be encapsulated like "resting spores" - and spread as "swarm spores", leading to metastases in the body.

It's said that similar, repeated stimuli or irritations from outside - of all kinds - can initiate cancer, one-sided pressure and even distilled water repeatedly brushed on laboratory animals. This could be translated to a suppression of "the whole" and with it the integrating center in the organisms? The organism's response to the stimuli may lead to exhaustion that in reality depends on "all the rest" that doesn't get activated, the whole that are dismissed in favor of the part.

11. Prokaryotic - Eukaryotic single-cells:
Here about theories of how eukaryotic cells emerged. Other aspects in additional file (No.. b) to Aviation,

Prokaryotic unicellular organisms (PKc) as blue-green algae and bacteria lack nuclei with membranes and mitochondria. Eukaryotic cells (EKc) have both these membranes and several other organelles in cytoplasm.
   PKc have similarities with the embryological blastula stage of multicellular organisms, EKc with the gastrulation stage with several inner tied off parts of membrane à la "vesicles" to creation of specialized tissues and separate centers.
   Compare too the evolution from 1- to 2- to 3-layer organisms.

It's a common view on embryological development that it reflects earlier stages of evolution. We could presume that the same principles for 'evolvement/involvement' are prevalent on underlying levels as on superposed ones.
   Thus, it becomes a possible hypothesis that development from algae and bacteria to EKc occurred in a corresponding way, through invagination (of material) of their cell membranes.
   But why should it take billions of years?

Another hypothesis among scientists is that mitochondria and chloroplasts are bacteria and algae that have immigrated into or become incorporated by bigger, heterotrophic cells - and then lost their capacity for independent existence. (According to some theory the nucleus itself should have been an outsider that had immigrated into another PKc before chloroplasts.).
   Similarities between ribosomes in EKc and PKc have been one reason for this hypothesis. However, it doesn't explain emergence of the nuclear membrane in EKc. It's also pointed out that several components of mitochondria "curiously enough" are synthesized in cytoplasm of EKc outside mitochondria.
   Such things seems sooner to support the other hypothesis among scientists about invaginations of own membrane of the gastrulation type. Similarities in ribosomes could be regarded from the aspect that organelles of PKc and EKc make up analogous dimension steps on different levels. And cilia have also a little DNA but are not attributed or suspected to have had any earlier independent existence.

There are other facts that seem to favor the theory about invaginating cell membrane. There can be found such invaginations to "mesomeres" already in PKc and certain structures analogous with an endoplasmic reticulum (Bc p. 290). The theory needs of course another explanation of DNA in mitochondria and chloroplasts, but already in PKc smaller, ring formed DNA-strands (plasmids) exist outside the bigger DNA-thread (Fc p. 168 f.).

The relation between EKc and PKc has features of the type center — anticenter, also the one between higher and lower d-degrees but this relation is ambiguous. Certain features point to PKc as of higher d-degree in our interpretations: the use of both L- and D-forms of amino acids in their membrane proteins, the less polarized (not sexual) cell divisions and the less amount of inner motions for instance (see here). In other respects PKc have the features of anticenter. They remain a multitude of single-cells, while EKc leads further to multicellular organisms, to a new level. (Cf. the small satellite cells in he peripheral nervous system surrounding the bodies of big nerve cells.).
   This ambiguity could follow from a dimension chain, where debranched degrees in first higher steps meet "the other way around" from anticenter, the 00-pole, inwards.
   A general postulate or aspect on the dimension model for evolution is also the stepwise building in of the 00-pole, the anticenter.

Perhaps the two different hypotheses above can be seen as only two aspects on the same development, only two opposite directions of reading a dimension chain, illustrated in the figure below.
   1) Prokaryotic cells as created from debranched degrees in higher steps, meeting the other way around in synthesizing direction inwards 3 ← 2 ← 1←0/00, immigrating into cells from higher d-degrees: a reading of the chain inwards.
   2) Pre-eukaryotic cells from higher d-degree steps 5 →> 4 →> 3 meet at their outer surface (d-degree 2 ) structures from steps 2 ← 1←0/00, which get enclosed through invaginations. This is a more or less equivalent description than that in point 1, reminding of the gastrulation of multicellular embryos from blastula stage.
   An ambiguity appearing in step 3 - 2.

Fig C-26-162

The similar ambiguous relations appear among multicellular organisms when it concerns 1-, 2- and 3-layer animals.

The two theories become connected with the two ways to look at the dimension chain, "horizontally" as a "straight chain" in synthesizing direction inwards - or "vertically" as in the loop model, outward - inward directions meeting in step 3-2: d-degree 5 polarized a) 0-00, b) 4-1, c) 3-2.

Should this view imply that EKc perhaps existed much earlier in time than believed, that both kinds EKc and PKc eventually emerged as c-ac-poles simultaneously? In a relation one to many? Archae bacteria, now regarded as an own phyla, show certain features similar to both PKc and EKc.

One question is why only one (or some?) PKc transformed to EKc. A special change in outer environment? A mutation? Something that got wrong at cell division …? A kind of "neoteny" in the evolution of chromosomes? - Or just an underlying principle, implying steps towards more complicated structures as in a dimension chain, in similarity with how classes of substances develop from strings towards higher d-degrees in shape: 3 ← 2←1 ←0?

Invaginating layers and cells as trapped light?
A related speculation concerns the layers of different substances that surround cell membranes of many organisms: outer layers of proteins, glycolipids, mucopolysaccharides and such combinations of the more elementary classes of molecules.
   Could perhaps such layers have been a first phase during evolution? (Compare the hexagonal pattern in first figure above) Layers that invaginated and closed and made outer kinds of molecules inner ones? A pole exchange center - anticenter in our model. This in the same way - and by the similar forces - as the blastula transforms to gastrula in multicellular organisms? In the dimension model, as said above, one general aspect is the stepwise "building-in" of the 00-pole.

And what about strings of nucleotides? It's a bit curious that DNA as chromatids on photos seem mostly attached to the inside of nuclear membrane. It's said that DNA-thread in bacteria is attached to their cell membrane. Couldn't DNA also primarily have been formed on the outside of a membrane layer, exposed to light, and then have invaginated? Chromosomes as molecules for refraction of light could on an early stage of evolution easily have been affected by chemical environment at a surface? Chromosomes as "substantiated light", "lumosomes"? (Autotrophic bacteria that used other energy sources should in that case have been a later adaptation?)
   The light-capturing chloroplasts with DNA are for instance located along the surface layer of the cell wall in Spirogyra algae, and development of chloroplasts is dependent on light exposition. The respiratory chain in mitochondria with DNA is attached to its cell membrane.
   Steroids get bound to lipid membranes but binds also to DNA.

With the mentioned facts it seems possible to imagine that DNA (or rather RNA) once were located and constructed on the outside of a lipid membrane and then through invaginations became the inside - immigrated. Cf. on the multicellular level invagination of the neural tube: outside becomes inside, environment built-in. Cells as trapped light?
   Cf. Evolution, the turn inside-out of blastula in embryology of some sponges and similar processes in colonies of flagellates.

12. Some final words:

What could have been the real root of a first cell? We may speculate about an original conglomerate, a multidimensional network, something like the principle in the hexagonal pattern in figure 1 above, where different stereometric configurations and points of refraction in different angles and readings of patterns - or restratifications - have given the different classes of substances and combinations of them. And that meshes in the network as matrices or the like could have been the origin of the coupling between proteins and codon bases, bases where parts of the rings simultaneously make up atoms in amino acids. Structure relations in the network then through polarizations and substantiations developed to processes of syntheses for different substances.

Yet, what could have served as a very first "center" and first "anticenter", poles within which a cell developed, in a sense that agrees with the dimension model?
   An eventual complex network or series of layers is hard to see as such poles out of some 5-dimensional pre-unit. Nor does DNA resemble such a first center.

- Just energy in some form, serving as center? Corresponding to how amino acids and bases etceteras on an underlying level are shaped from elementary molecules in Miller-Urey type of experiments?
- Or one single hydrogen atom H, the inversion of which appears as first anticenter? As guide for a pure mathematical, organizing principle underlying the development? (Cf. about quotient e/p in files here and here about the genetic code. About inversion also file 1/7; 7 "not developed" d-degrees according to the string theory.
- Or a P-group, inorganic phosphorus (H3PO4), an atom as P with valence 5 as core for condensation, functioning as the speck of dust for an ice crystal around which it gets organized?
- Or just organic molecules trapped in a metal environment as first anticenter? The polarity of metals - non-metals, defined by the "octet rule", enough as definition of first center-anticenter poles?

A center defines directions - outwards / inwards. In chemical terms for instance hydrophilic - hydrophobic directions. In next step  in the model a spherical structure versus a radial one gets defined.
     Within the cell as a whole, a unit, interpreted as a whole dimension chain, each step can according to primary postulates develop to whole secondary chains, the steps in these to tertiary chains etceteras.

Fig C-27-143-2

It gives an exponentially increasing number of directions and structures within the cell and increasing number of motional moments as processes.
   The hypothetical conglomerate of both lipid layers and nucleotides and proteins could then be imagined to polarize, creating increasing distances within these poles, with development of circular processes from the different steps. Something like the embryological gastrulation of a eukaryotic, multicellular organism.


A note:
It's hard to believe that all cells on the Earth derive from just one single cell, even if it's unknown how a cell is born in other ways than through duplication. Why then look for life on other distant planets! It's illogical.
   Either there exist a principle of Nature of only one single cell as one center of Universe (which happened to be here). Or life appeared under right circumstances on a lot of places - on the Earth and other planets.

To an extra link: Levels from Micro- to Macrocosm


© Åsa Wohlin
Free to distribute if the source is mentioned.
Texts are mostly extractions from a booklet series, made publicly available in year 2000

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